Problem: N different natural numbers are given. If you select four different ones and set them as $ A $, $ B $, $ C $, $ D $, the following formula

$ \ Frac {A + B} {C --D} $



I want to find the maximum value of.




Given N different natural numbers, choose 4 different from them and create a program to find the maximum value of the above formula.



Input

The input is given in the following format.


N
a1 a2 ... aN


The number N (4 ≤ N ≤ 1000) of natural numbers is given in the first line. The value ai (1 ≤ ai ≤ 108) of each natural number is given in the second line. However, the same natural number does not appear more than once (ai ≠ aj for i ≠ j).

Output

Outputs the maximum value of the above formula as a real number for a given N natural numbers. However, the error must not exceed plus or minus 10-5.

Examples

Input

10
1 2 3 4 5 6 7 8 9 10


Output

19.00000


Input

5
22 100 42 3 86


Output

9.78947


Input

6
15 21 36 10 34 5


Output

18.00000


Input

4
100000 99999 8 1


Output

28571.285714

Solution (in CPP):

Solution:
#include<iostream>
#include<algorithm>
#include<climits>
#include<cmath>
#include<cstdio>
#include<cstdlib>
#include<ctime>
#include<string>
#include<cstring>
#include<vector>
#include<stack>
#include<queue>
#include<set>
#include<map>
#include<bitset>

using namespace std;

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int, int> i_i;
typedef pair<long long, int> ll_i;

#define PI 3.141592653589793238462643383279
#define mod 1000000007LL
#define rep(i, n) for(i = 0;i < n;++i)
#define rep1(i, n) for(i = 1;i < n;++i)
#define per(i, n) for(i = n - 1;i > -1;--i)
#define int(x) int x; scanf("%d",&x)
#define int2(x, y) int x, y; scanf("%d%d",&x, &y)
#define int3(x, y, z) int x, y, z; scanf("%d%d%d",&x, &y, &z)
#define int4(v, x, y, z) int v, x, y, z; scanf("%d%d%d%d", &v, &x, &y, &z)
#define int5(v, w, x, y, z) int v, w, x, y, z; scanf("%d%d%d%d%d", &v, &w, &x, &y, &z)
#define pri(x) cout << (x) << "\n"
#define pri2(x, y) cout << (x) << " " << (y) << "\n"
#define pri3(x, y, z) cout << (x) << " " << (y) << " " << (z) << "\n"
#define pb push_back
#define mp make_pair
#define all(a) (a).begin(),(a).end()
#define kabe puts("---------------------------")
#define kara puts("")
#define debug(x) cout << " --- " << (x) << "\n"
#define debug2(x, y) cout << " --- " << (x) << " " << (y) << "\n"
#define debug3(x, y, z) cout << " --- " << (x) << " " << (y) << " " << (z) << "\n"
#define X first
#define Y second
#define eps 0.0001
#define prid(x) printf("%.15lf\n", x)

int a[1000];

signed main(void){
  int i, j;
  for(int testcase = 0;testcase >= 0;testcase++){
    int(n);
    rep(i, n)scanf("%d", a+i);
    sort(a, a + n);
    double res = 0.0;
    rep1(i, n){
      int t, b = a[i] - a[i - 1];
      if(i == n - 1)t = a[n - 3] + a[n - 4];
      else if(i == n - 2)t = a[n - 1] + a[n - 4];
      else t = a[n - 1] + a[n - 2];
      res = max(res, (double)t / (double)b);
    }
    prid(res);

/*/

//*/ break;
  }
  return 0;
}